A small COVID testing location has a single reception desk. The time between two arriving people equals on average 3.5 minutes (Poisson arrival process). Exactly 27 people per hour can be helped at the desk. What is the average number of clients w
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A small COVID testing location has a single reception desk. The time between two arriving people equals on average 3.5 minutes (Poisson arrival process). Exactly 27 people per hour can be helped at the desk. What is the average number of clients waiting for their turn (so excluding clients who are actually being helped)? (Round your answer to two decimals)
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- Only typed answer otherwise leave it Renuka Jain's Car Wash takes a constant time of 4.54.5 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 1212 per hour. Renuka wants to? know: ? a) The average wait time in the line ?= __________(round your response to two decimal? places). ? b) The average number of customers waiting in the line ?= ________ cars ?(round your response to two decimal? places).Students arrive at the Administrative Services Office at an average of one every 20 minutes, and their requests take, on average, 12 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. What percentage of time is Judy idle? Note: Round your answer to 1 decimal place. How much time, on average, does a student spend waiting in line? Note: Do not round intermediate calculations. Round your answer to 1 decimal place. How long is the (waiting) line on average? Note: Round your answer to 2 decimal places. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? Note: Do not round intermediate calculations. Round your answer to 2 decimal places.Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take, on average, 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. What percentage of time is Judy idle? Note: Round your answer to 1 decimal place. How much time, on average, does a student spend waiting in line? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. How long is the (waiting) line on average? Note: Round your answer to 2 decimal places. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? Note: Do not round the intermediate calculations. Round your answer to 2 decimal places.
- Students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take, on average, 4 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. a. What percentage of time is Judy idle? (Round your answer to 1 decimal place.) b. How much time, on average, does a student spend waiting in line? (Do not round intermediate calculations. Round your answer to 1 decimal place.) c. How long is the (waiting) line on average? (Round your answer to 2 decimal places.) d. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? (Do not round intermediate calculations. Round your answer to 4 decimal places.)Find a Doctor is a small startup that helps people find a physician who best meets their needs (location, insurance accepted, etc.). During a “slow” time for it, it has 8 staff members taking calls from customers. On average, one call arrives every 5 minutes (with a standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27.00 minutes). How long does one of their customers spend, on average, waiting on hold before he or she can start speaking to a representative?A Northwest Airlines ticket counter forecasts that 30 people per hour will need to check in. It takes an average of 1.5 minutes to service a customer. Assume that interarrival times and service times are exponential and that all customers wait in a single line for the first avaliable agent.If we want the average time a customer spends in line and in service to be 3 minutes or less, how many ticket agents should be on duty?
- What is the average utilization of the servers in a system that has three servers? On average, 15 custom-ers arrive every 15 minutes. It takes a server exactly three minutes to wait on each customer.Joe’s market is a small grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag. If Joe does not want the average waiting time in the queue to exceed 5 minutes, what would you tell Joe about his current system? Back up your statement with quantitative information and assumptions.Customers arrive at the company's service office at an average of one every 20 minutes. Their requests take, on average, 15 minutes to be processed. The service counter is staffed by only one employee, who works six hours per day. Assume Poisson arrivals and exponential service times. What model should you use? What percentage of time is the employee idle? How long is the waiting line, on average? How much time, on average, does a customer spend waiting in line? What is the probability that an arriving customer, just before entering the office, will find at least one other customer waiting in line?
- A local fast-food restaurant wants to analyze its drive-thru window. At this time, the only information known is the average number of customers in the system (4.00) and the average time a customer spends at the restaurant (1.176 minutes). What are the arrival rate and the service rate?Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 6 haircuts per hour. a) The average number of customers waiting for haircuts = ? enter your response here customers (round your response to two decimal places). b) The average number of customers in the shop = ?customers (round your response to two decimal places). c) The average time a customer waits until it is his or her turn = ? enter your response here minutes (round your response to two decimal places).A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution. How much of that time is spent waiting for service?